Can I have have help algebraic terms like factorising and expanding brackets

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Expanding brackets is a fundamental algebraic skill. When we have a number or variable outside brackets, we multiply it by each term inside. For example, 3 times the quantity x plus 4 equals 3 times x plus 3 times 4, which gives us 3x plus 12. The FOIL method helps us expand two binomials. FOIL stands for First, Outer, Inner, Last. For example, when expanding x plus 2 times x minus 5, we multiply: First terms x times x equals x squared, Outer terms x times negative 5 equals negative 5x, Inner terms 2 times x equals 2x, and Last terms 2 times negative 5 equals negative 10. Combining these gives x squared minus 5x plus 2x minus 10, which simplifies to x squared minus 3x minus 10. Factorising is the reverse of expanding brackets. We look for the greatest common factor first. For 6x squared plus 9x, we find the GCF by breaking down each term. 6x squared equals 2 times 3 times x times x, and 9x equals 3 times 3 times x. The greatest common factor is 3x. So we can write 6x squared plus 9x as 3x times the quantity 2x plus 3. To factorise quadratic trinomials like x squared plus 5x plus 6, we need two numbers that multiply to give ac and add to give b. Here a equals 1, b equals 5, and c equals 6. So ac equals 6. We need numbers that multiply to 6 and add to 5. The numbers 2 and 3 work: 2 times 3 equals 6, and 2 plus 3 equals 5. Therefore, x squared plus 5x plus 6 factors as x plus 2 times x plus 3. The difference of squares is a special factorising pattern. When we have a squared minus b squared, it factors as a plus b times a minus b. For example, x squared minus 16 can be written as x squared minus 4 squared. Using our pattern with a equals x and b equals 4, this becomes x plus 4 times x minus 4. We can check this by expanding back to get x squared minus 16.